Is there a way to remove the Main Blog option from the My Blogs menu?

In multisite there is an admin dropdown menu called "My Blogs" that lists all the sites on the network that one has privileges on. The way I have my network configured regular users have no use of the dashboard of the main site, just the subsites. So the presence of that option confuses them. I'd like it not to appear to anyone that has subscriber status, and am wondering how to make that so. To be clear, I want them having access to all the other dashboards of which they have privileges, just not the dashboard of the main site.